# What is Piece-wise function: Definition and 16 Discussions

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1. ### Showing piece-wise function continuous

For this, , The solution is, However, should they not write ##f(x) = \cos x## on ##[\frac{pi}{4}, \infty)## Many thanks!
2. ### I How to evaluate the enclosed area of this implicit curve?

The implicit curve in question is ##y=\operatorname{arccoth}\left(\sec\left(x\right)+xy\right)##; a portion of the equations graph can be seen below: In particular, I'm interested in the area bound by the curve, the ##x##-axis and the ##y##-axis. As such, we can restrict the domain to ##[0...
3. ### MHB Continuous, discontinuous and piece-wise function

help me please to determine what are the equations i need tofinish my activity. Thankyou
4. ### MHB 1.8.4 AP Calculus Exam Integral of piece-wise function

image due to macros in Overleaf ok I think (a) could just be done by observation by just adding up obvious areas but (b) and (c) are a litte ? sorry had to post this before the lab closes
5. ### I Continuous Functions with Piecewise Functions

I have been working on this exercise 5 and kind of stuck how to start the problems. I would think to start with a graph, but I feel this is wrong. I am just stuck on a and b.
6. ### Mathematica FindMaximum function in Mathematica

I recently plotted a piecewise function: Plot[Piecewise[{{1 - Exp[-.002*t], 0 <= t < 120}, {-Exp[-.002*t] + Exp[-.002*(t - 120)], 120 <= t}}], {t, 0, 5000}, PlotRange -> {0, 0.25}] I then defined the function which I am calling q[t_] as follows: q[t_] := Piecewise[{{1 -...
7. ### Mathematica Troubleshooting Mathematica Plotting Problem

Homework Statement I've entered the following piecewise equation into Mathematica: Plot[Piecewise[{{sin (t), 0 <= t < \[Pi]}, {5 + 5 cos (t) + sin (t), \[Pi] <= t < 4*\[Pi]}, {10 cos (t) + sin (t), 4*\[Pi] <= t}}], {t, 0, 20*\[Pi]}] But I am getting a blank graph in return. I've proofread my...
8. ### How to Integrate g(x)=∫ƒ(t) dt from -5 to x | Homework Help

Homework Statement http://s23.postimg.org/wsj9e91wb/IMG_1334.jpg[/B] photo of the problem g(x)=∫ƒ(t) dt from -5 to x ƒ(t) = (0 if x < -5 5 if -5≤x<-1 -3 if -1≤≤x<3 0 if x≥3) (a) g(-8) = 0 (b) g(-4) = 5 (c) g(0) = ? (d) g(4) = ? Homework Equations ∫ƒ(x) from...
9. ### Finding A Constant To A Piece-Wise Function

The function is g(x) = (x^2 - a^2)/(x - a) if x doesn't equal a; and the second part is g(x) = 8 when x = a. The question asks for me to find a specific value for a so that the function might be continuous on the entire real line. I know that each part of the piece-wise function needs to...
10. ### Proving piece-wise function is one-to-one?

f: Z -> Z defined by f(x) = x/2 if x is even, (x-1)/2 if x is odd. Proof: If x is even: x1 = 2k1 x2 = 2k2 Suppose f(x1) = f(x2), then 2k1/2 = 2k2/2 k1 = k2 So if x is even, the function is one to one? Is this an okay proof for the first half of if x is even, then I just do the...
11. ### Proving Differentiability of a Piece-wise Function

1. Suppose f(x)=0 if x is irrational, and f(x)=x if x is rational. Is f differentiable at x=0? 2. the derivative= lim[h->0] [f(a+h)-f(a)]/h 3. I don't really know how to start, but I do know that between any two real numbers, there exists a rational and irrational number. So I'm...
12. ### Piece-Wise Function Continuity

Homework Statement Determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. f(x)= {x^3 if x < or = -2 {2 if x > -2 Homework Equations The conditions are that a function is said to be...
13. ### Simplifying Piecewise Functions: fg(x) and gf(x) Calculations

Homework Statement Function f and g are defined as follows : f(R)=R , f(x)=x^2 , g(R)=R , g(x)=x+1,x>=0 , -x , x<0 (its a piecewise function) . Find fg(x) and gf(x) . Homework Equations The Attempt at a Solution fg(x)= (x+1)^2 , x>=0 x^2 , x<0 gf(x)= x^2+1 , x>=0...
14. ### Continuity on a piece-wise function

[SOLVED] Continuity on a piece-wise function Problem: Suppose: f(x)=\left\{\begin{array}{cc}x^2, & x\in\mathbb{Q} \\ -x^2, & x\in\mathbb{R}\setminus\mathbb{Q}\end{array}\right At what points is f continuous? Relevant Questions: This is in a classical analysis course, not a...
15. ### Derivative of Piece-Wise Function

I am doing my calculus homework and two problems are holding me up. The first says: Using one-sided derivatives, show that the function f(x) = x^3, x_<_1 3x, x>1 does not have a derivative at x=1 Now it is painfully obvious that the function is not continuous at x=1. however, i...
16. ### Solving Piece-wise Functions: y=|x|+x Graph Explained

I'm doing a review of fuctions, and a nagging question popped up in my mind after completing this problem. After graphing y = |x| + x, express this equation as a piece-wise function with no absolute values. I did graph it; it was simple (following is a sketch without values)...